[1]} further establish a number of additional properties about the unhinged loss \(\phi ^\star \) ; most of these will not concern us, but one simple property, which we now explain, is relevant to our discussion in sec:example.
As above let \(v \in ^d\)  be the minimizer of \(_{(,) \sim {\cal D}}\left[\phi ((v\cdot ))\right]\)  subject to \(|| v || \le r\)  and let
\(v^{\prime } \in ^d\)  be the minimizer of \(_{(,) \sim \overline{\cal D}_{\eta }}\left[\phi ((v^{\prime }\cdot ))\right]\)  subject to \(|| v^{\prime } || \le r\) .
[1]} make the straightforward but useful observation that \(v\)  is the vector corresponding to a “nearest centroid classifier” (see
[3]}, [4]}, p. 181 of [5]}, and Section 5.1 of [6]}), i.e. we have
\( v = \alpha _{(,) \sim {\cal D}}[]\) 
